ON THE COLOURS OF THICK PLATES. 183 system of rings with both eyes at once, if the eyes be situated symmetrically with respect to the flame and its image. The rings so seen appear to be situated between the flame and its image. Let E be the right and E' the left eye, and suppose the head so placed that the line LL3 bisects EE' at right angles. On account of the similarity of position of the two eyes, the system of rings seen with one eye must be exactly like the system seen with the other, and therefore, in order that a single system may be seen with both eyes at once, it is necessary and sufficient that the axes of the eyes be directed to the centres of the respective systems. It has been shewn already that the projected place on the mirror of the centre of the system seen with either eye, suppose the right eye, bisects the line joining the projected places of the flame and its image. On account of the supposed srnallness of the obliquities, this is the same thing as saying that the centre of the system seen by the right eye appears in the direction of a line bisecting the angle LEL<y Similarly, the centre of the system seen by the left eye appears in the direction of a line bisecting the angle LE'LZ. In order therefore that a single system only may be seen, the axes of the eyes must be made to converge to the point in which the bisecting lines intersect LL<]} arid therefore the system of rings will appear to be situated between the flame and its image. Since the angles LEL^ LE L,^ are bisected by- the axes of the eyes when the system of rings is seen single, it follows that the flame and its inverted image arc each seen, double, in such a manner that the erect flame seen by either eye is superposed on the inverted flame .seen by the other. This agrees with observation : in fact, I was led by experiment to the above rule for determining the apparent position of the rings before I had deduced it from theory. The observation was made when the flame was in front of its image, in which case the position of the rings in space appears more definite than when the image is in front of the flame.